Abstract
Abstract In [T. Okada, Birational Mori fiber structures of ℚ \mathbb{Q} -Fano 3-fold weighted complete intersection, Proc. Lond. Math. Soc. (3) 109 2014, 6, 1549–1600], we proved that, among 85 families of ℚ \mathbb{Q} -Fano threefold weighted complete intersections of codimension two, 19 families consist of birationally rigid varieties and the remaining families consists of birationally non-rigid varieties. The aim of this paper is to study systematically the remaining families and prove that every quasismooth member of 14 families is birational to another ℚ \mathbb{Q} -Fano threefold but not birational to any other Mori fiber space.
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